A numerical investigation of some key factors for the simulation of convection-dominated melting

Abstract In the struggle for a more sustainable economy, thermal energy storage is a relevant solution either for solving the intermittency that is intrinsic to many renewable power plants, or for promoting energy efficiency and the reuse of waste heat. Among the available storage technologies, some rely on latent heat with solid-liquid phase transitions, where natural convection often plays a significant role. For practical and historical reasons, this problem is usually modeled through diffuse interface methods involving two fundamental effects that require specific treatment. The first one concerns canceling the velocity field in the solid phase, usually handled with a penalization term. The second one deals with the phase change property, and is roughly connected to the melting temperature or temperature range of the phase change (pure substances and mixtures respectively) and associated latent heats. Two main issues are associated with these parameters: firstly, there is no reliable method to unambiguously determine them, and secondly and more importantly, their influence and mutual interaction have received little attention. The present study aims to tackle these issues and to help non-specialists or engineers to have a clearer view of the possible mistakes or confusions that can easily pollute such simulations. As a rule of thumb, it is thus demonstrated that the proper definition of the temperature range for the phase change is a cornerstone, equally significant with the latent heat. Moreover, the penalization term (i.e. the mushy zone constant) can compete with or hide the effects of this transition range. This means that its value is not independent of the temperature range in which the phase transition occurs. Consequently, its value should be set carefully.